Curtis E RenshawTele-Consultants, Inc. 4080 McGinnis Ferry Rd., Suite 902,

Alpharetta, GA 30005

crenshaw@teleinc.com

The Gravitational Potential for a Moving Observer,

Mercury’s Perihelion, Photon Deflection and

Time Delay of a Solar Grazing Photon

h

c

v

Motion induced Blue-Shift

Gravitational Red-Shift

Pound-Rebka Experiment

Resolution

Fundamental Result

Fundamental Result

c’ – takes into account relative motion with respect to source

h’ – takes into account effective changes in h with time

g’ – takes into account motion induced effects on gravitational potential

General Doppler Shift Equation

h h

dhv

c + v c

Radial Motion

Motion induced Doppler Gravitational Red-Shift

Radial motion (along gravitational line) has no effect on the measured gravitational red-shift or on the effective gravitational potential for such motion.

Radial Motion

h

c

v

c’

v

cc’

Transverse Motion

Transverse motion has an effect on the measured gravitational red-shift and on the effective gravitational potential for such motion.

Motion induced Doppler Gravitational Red-Shift

The Generalized Gravitational Potential for a Relative Motion

Transverse MotionThe Generalized Potential

GPSDoes the Principle of Equivalence imply that a free-fall observer should see the same gravitational red-shift at a particular point in space as a stationary observer?

LaGrangian

Equations of Motion

The Perihelion Shift of Mercury

Photon Deflection

Time Delay of Solar Grazing Photon

Irwin Shapiro – 1964

n

’n

d

Rr

Time Delay of Solar Grazing Photon

d

Rr

Time Delay of Solar Grazing Photon

d

Rr

Time Delay of Solar Grazing Photon

d

Rr

Time Delay of Solar Grazing Photon

d

Rr

For distances on the order of Earth-Mars, Dd is approximately 19 km, resulting in a time delay of about 250ms, which is what Shapiro observed.

Conclusion

• Using only Newtonian Mechanics and the Principle of Equivalence, a Dynamic Gravitational Potential was developed to account for relative motion between bodies.

• This modified Newtonian potential has been demonstrated to fully account for three “tests” of general relativity:

• Mercury’s perihelion shift of 43” per century,

• The deflection of a solar grazing photon

• The time delay of a solar grazing photon